I do not believe it is possible. As it states in the product documentation, "AlchemyData News indexes 250k to 300k English language news and blog articles every day with historical search available for the past 60 days."

That will tell me if the news API has indexed "WSJ". Doesn't that mean that the API is searching a list/table/data structure somewhere for the domain "WSJ"? If it can do that, then why couldn't it provide the list of the domains it's searching?

Also, just from a sales perspective, why would anyone purchase this if they don't know what's in it? In my case, I'd like to use a news API for analysis of financial news. To decide if Alchemy is the right tool, I need to know which financial news sites are included.

From a general news perspective, there's plenty of reason to know the sources as well. Are they left or right biased? What is the geographical coverage? Are there local and regional outlets included?

This question has been closed with this answer, this does not answer the question. The linked question only shows how to validate that a source has been ingested, not to define the list of available sources